Analytical and numerical study on grating depth effects in grating coupled waveguide sensors

The in-coupling process for grating-coupled planar optical waveguide sensors is investigated in the case of TE waves. A simple analytical model based on the Rayleigh--Fourier--Kiselev method is applied to take into account the depth of the grating coupler, which is usually neglected in the modeling. Analytical expressions are derived both for the position and width of the in-coupling peaks to illustrate the effects of grating depth on the guided mode resonances in grating coupled waveguide sensors. Numerical computations verify the model for shallow gratings both in terms of peak shape and position and provide the limitations for the analytical formulas.